Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 24


$-\dfrac{3 \sqrt 3}{2} -\dfrac{3}{2}\ i$

Work Step by Step

We know from the unit circle that: $\cos 210^{\circ}=-\dfrac{\sqrt 3}{2}$ $\sin 210^{\circ}=\dfrac{1}{2}$ Thus,, we simplify the given expression as follows: $3[\cos (210^{\circ})+i \ \sin (210^{\circ})] \\=3 (-\dfrac{\sqrt 3}{2} -i \cdot\dfrac{1}{2}) \\=3 \left(-\dfrac{\sqrt 3}{2}\right) - 3\left(i \cdot\dfrac{1}{2}\right) \\=-\dfrac{3 \sqrt 3}{2} -\dfrac{3}{2}\ i$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.